Inertial Frame of Reference

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Inertial Frame of Reference

a frame of reference in which the law of inertia is valid: a mass point is at a state of rest or uniform linear motion when it is not acted on by any forces (or when it is acted on by balanced forces). Any frame of reference that is moving translationally, uniformly, and rectilinearly with respect to an inertial frame of reference is also an inertial frame of reference. Consequently, in theory any number of fully valid inertial frames of reference may exist with the important property that in all such frames the laws of physics are identical (the so-called relativity principle). In addition to the law of inertia, in any inertial frame of reference Newton’s second law and the laws of conservation of momentum and of angular momentum, as well as the law of motion of the center of inertia (or center of mass), are also valid for closed systems (systems not subject to external influences).

If a frame of reference does not move uniformly and linearly with respect to an inertial frame of reference, it is a noninertial frame, and neither the law of inertia nor the other laws mentioned above are observed within it. This is because even in the absence of acting forces a mass point will have an acceleration with respect to a noninertial frame of reference as a result of the accelerated translatory or rotational motion of the frame of reference itself.

The concept of an inertial frame of reference is a scientific abstraction. A real frame of reference is always connected with some specific body, such as the earth or the body of a ship or aircraft, with respect to which the motion of various objects is studied. Since there are no stationary bodies in nature (a body that is stationary with respect to the earth will move together with it under acceleration with respect to the sun and stars), any real frame of reference may be considered as an inertial frame of reference only to various degrees of approximation. The so-called heliocentric (stellar) system, with its reference point at the center of the sun (or, more accurately, at the center of mass of the solar system) and its coordinate axes directed toward three stars, may be considered an inertial frame of reference to a very high degree of accuracy. Such a frame of reference is used primarily in problems of celestial mechanics and astrogation. In practice a frame rigidly connected to the earth or, in cases that require greater accuracy (such as gyroscopy), a system with its origin at the center of the earth and its axes oriented toward the stars may serve as an inertial frame of reference for the solution of most technical problems.

In converting from one inertial frame of reference to another, Galilean transformations are valid for spatial coordinates and time in classical Newtonian mechanics, and Lorentz transformations are used in relativistic mechanics (that is, for rates of motion close to the speed of light).

We can measure the rate of changes with clocks, but according to Special Relativity (SR), the value obtained from this measurement is relative to the inertial frames of the observer and of that which is observed.

More advanced applications - including gravitational orbits, rigid body dynamics and mechanics in rotating frames - are deferred until after the limitations of Newton's inertial frames have been highlighted through an exposition of Einstein's Special Relativity.

On the contrary, in the Lorentz transformations, given any inertial reference frame (K', K, or any other inertial frame), there is c' = c and, hence, the velocity of light in the inertial frame K, being measured by the observers located in the inertial frames K' and K is always the same.

where the angle [alpha]' is counted from the x'-axis in the moving inertial frame K'.

These just alluded situations should be appreciated by consideration (prevalently or even asymptotically) of Einstein's posulate of relativity, which states [3] that the inertial frames of references are equivalent to each other, and they cannot be distinguished by means of investigation of physical phenomena.

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